English

Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry of Domains

Complex Variables 2007-05-23 v4 Group Theory Metric Geometry

Abstract

This paper lays down a foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theory based on the representation theory of SL(2,R) group. We describe here geometries of corresponding domains. The principal role is played by Clifford algebras of matching types. Keywords: analytic function theory, semisimple groups, elliptic, parabolic, hyperbolic, Clifford algebras

Keywords

Cite

@article{arxiv.math/0410399,
  title  = {Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry of Domains},
  author = {Vladimir V. Kisil and Debapriya Biswas},
  journal= {arXiv preprint arXiv:math/0410399},
  year   = {2007}
}

Comments

14 pages, AMS-LaTeX, 31 PS graphcs in 7 Figures; v2--the missing PS file is included now; v3 minor corrections, reference added; v4 numerous misprints corrected

R2 v1 2026-07-22T17:11:19.136Z